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Elliptical Tube offers a range of functions and documentation to aid in analyzing and visualizing elliptical tubes. The package supports complex shape simulations and includes supplementary materials to help users navigate its functionality effectively.

The repository is linked to the publications mentioned below.

Article: “The Mean Shape under the Relative Curvature Condition”

Taheri, Mohsen, Stephen M. Pizer, and Jörn Schulz. Journal of Computational and Graphical Statistics.

PhD thesis: “Shape Statistics via Skeletal Structures”

Mohsen Taheri Shalmani, University of Stavanger, Norway.

Cite

@article{taheri2025mean,
  title={The Mean Shape under the Relative Curvature Condition},
  author={Taheri Shalmani, Mohsen and Pizer, Stephen M and Schulz, J{\"o}rn},
  journal={Journal of Computational and Graphical Statistics},
  pages={1--21},
  year={2025},
  publisher={Taylor \& Francis},
  url={https://doi.org/10.1080/10618600.2025.2535600}
}

ETRep R Package

ETRep R package is designed for the analysis of elliptical tubes, applying the Relative Curvature Condition (RCC) for enhanced shape analysis. This package provides tools for computational and graphical methods relevant to studies involving tubular structures and shape simulation, making it a handy framework for research in fields such as biological shape analysis, robotic arm transformations, and geometry.

Citation

If you use ETRep in your research, please cite it as follows: ## Cite

@Manual{ETRep2024,
  title = {R package ETRep: Analysis of Elliptical Tubes Under the Relative Curvature Condition},
  author = {Taheri Shalmani, Mohsen and Schulz, J{\"o}rn and Pizer, Stephen M},
  year = {2024},
  note = {R package},
  doi  = {10.32614/CRAN.package.ETRep},
  url = {https://CRAN.R-project.org/package=ETRep}
}

https://doi.org/10.32614/CRAN.package.ETRep

Installation

To install ETRep from CRAN, use:

install.packages("ETRep")

CRAN Archive

The previous versions are available at:

https://cran.r-project.org/src/contrib/Archive/ETRep/

Images from the article

Fig0 Fig1 Fig2 Fig3

Visualization of the surface mesh of two elliptical tubes

Fig6

A depiction of the simulated ETReps and their mean shape.

Fig4
Fig4

Visualization of a valid transformation without any self-intersections

Fig5
Fig5